Introduction

This analysis explores the relationships of agricultural commodity loss, at a county level, from 1989-2015, for the 26 county region of the Palouse, in Washington, Idaho, and Oregon. Here we explore the entire range of commodities and damage causes, identifying the top revenue loss commodities and their most pertinent damage causes - as indicated from the USDA’s agricultural commodity loss insurance archive.

We perform several steps to examine the full set of data, and to narrow down factors to a usable form, for mixed modeling analysis.

Step 1. Data Preparation: Loading and Transforming data. Here we load commodity loss data, and aggregate by differing factors, so we can examine losses on an annual basis, by county, damage cause, and commodity.

Step 2. Study Area Overview. We narrow down our data to the 26 county palouse region, and display a study area map for perspective.

Step 3. Summary Overview of total revenue by Commodity. We summarize all commodity insurance loss by commodity - so we can determine the top revenue loss commodities for a filtered examination.

Step 4. Summary Overview of total revenue by Damage Cause. Similarly to Step 3, we summarize all insurance loss by the cause of the damage, so we can determine which damage causes are resulting the the majority of insurance loss.

Step 5. Refinement of data to top revenue commodities, and Damage Causes that are most impactful. Given Steps 3 and 4, here we narrow down our dataset to only examine those top commodities and most impactful damage causes.

Step 6. Exploratory Analysis of top commodities individually, to see variations by damage cause. In Step 6, we now examine the top commodities individually, looking at how insurance loss varies by damage cause, by county, and by year.

Step 7. Resolving missing data. In some instances, we have missing data, and in other instances, zero value data is not missing, but rather, there is just no values/loss claims for a particular commodity or damage cause - i.e. a commodity was grown in county X, but there was no drought claims, vs. there were no drought claims becuase, the commodity itself was not grown at all. In Step 8, we attempt to resolve missing data issues for our Step 8 analysis.

Step 8. Individual Commodity Mixed Model Analysis. In Step 8, we perform a mixed modeling analysis, using a two step hurdle model technique to address zero-inflated data.

Step 1. Data Preparation: Loading and Transformation data

The first step is to load Pacific Northwest agricultural insurance commodity loss data, aggregate by county, damage cause and commodity, remove zeros, transform the loss values ($) into cube root and logrithmic outputs, and scale and center the data.


Step 2: Study Area Overview - 26 County Palouse Region

The following is the 26 county Palouse region that this analysis is focusing on.


Step 3: Summary Overview of Insurance Loss by Commodity: 1989 - 2015 for the Palouse

Below is a breakdown of total insurance loss by COMMODITY for the 26 county Palouse region, from 1989 - 2015.

In order to reduce our dataset analysis, we are limiting our examination to only the cropping systems that incurred the most revenue loss - which are: 1. Wheat; 2. Apples; 3. Cherries; and 4. Dry Peas


STEP 4: Total Revenue by Damage Cause, 1989 - 2015 for the Palouse

Below is a breakdown of total insurance loss by DAMAGE CAUSE for the 26 county Palouse region, from 1989 - 2015.

In order to reduce our dataset analysis, we are limiting our examination to only the DAMAGE CAUSES that are incurred by the combination of the FOUR main commodities: wheat, apples, cherries, and dry peas.

STEP 5: Damage Cause Overview for EACH of the four top commodities


Top Damage Causes for APPLES, 1989-2015 for the Palouse Region


Here we see that: 1. Hail, 2. Frost, 3. Freeze, and 4. Cold Wet Weather are the predominant causes for loss for APPLES.


APPLES interaction plot loss vs year for all damage causes, all Palouse counties


Here we see that hail damage causes are tending to be quite high in 2006, 2012, and 2015.


Top Damage Causes for WHEAT, 1989-2015 for the Palouse Region

Here we see that: 1. Drought, 2. Heat, 3. Decline in Price, 4. Frost, 5. Hail, and 6. Freeze are the predominant causes for loss for WHEAT


WHEAT interaction plot loss vs year for all damage causes, all Palouse counties

Top Damage Causes for CHERRIES, 1989-2015 for the Palouse Region

Here we see that: 1. Excessive Moisture/Precipitation/Rain, 2. Freeze, 3. Frost, 4. Cold Wet Weather, are the predominant causes for loss for CHERRIES.

CHERRIES interaction plot loss vs year for all damage causes, all Palouse counties

Top Damage Causes for DRY PEAS, 1989-2015 for the Palouse Region

Here we see that: 1. Drought, 2. Heat, 3. Hail, 4. Excessive Mositure/Precipitation/Rain, are the predominant causes for loss for DRY PEAS.


DRY PEAS interaction plot loss vs year for all damage causes, all Palouse counties

Step 6: Exploratory Data Analysis


APPLES Boxplots

WHEAT Boxplots

CHERRIES Boxplots

DRY PEAS Boxplots

Step 3: Missing Data Examination


WHEAT Missing Data examination by damage cause, year, and county, using two dimensions

APPLES Missing Data examination by damage cause, year, and county, using two dimensions

CHERRIES Missing Data examination by damage cause, year, and county, using two dimensions

DRY PEAS Missing Data examination by damage cause, year, and county, using two dimensions

## Error in ezDesign(palouse_sumloss_aggregate_drypeas, year, damagecause, : unused argument (las = 3)

Step 4: Filling in missing data and other transforms for model runs

In this step, we fill in missing data for damage cause where commodity loss exists in a county. For example, if wheat is grown in a county for a particular year, but NO wheat loss claims were submitted - we consider this a zero (there where zero claims - vs this data being missing). We do this in order to ensure that we have as complete a dataset as possible.


Hurdle Mixed Models

Hurdle model techniques allow us to address zero inflated datasets, by first running a logstical regression model to determine the probability of zeros occuring. Then we use the non-zero values in a separate, mixed model. In this instance, we use county as a random effect.

In our two part hurdle model, we identify zero values - that is, counties and years that have zero loss for particular damage causes for apples. Previously we removed counties that we have determined have no apples being grown - based on known crop yield data. The counties we are identifying are those where we KNOW apples are being grown, but in some instances, there are no loss claims being filed in particular years.

As such, these are not missing data, but actual zero values that we do not want to exclude from our model. However we want to be able to use a normalized distribution that is not positively skewed/zero inflated.


Hurdle Model - APPLES

Here we run our hurdle technique for APPLES. Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?

##          llh      llhNull           G2     McFadden         r2ML 
## -297.6154204 -473.1882133  351.1455859    0.3710422    0.3798222 
##         r2CU 
##    0.5245698
## 
##  Hosmer and Lemeshow goodness of fit (GOF) test
## 
## data:  alllevs2_apples$non_zero, fitted(m1)
## X-squared = 10.439, df = 8, p-value = 0.2356

##                                   GVIF Df GVIF^(1/(2*Df))
## year                             1.164 14           1.005
## damagecause            80589335779.706  6           8.107
## county                       15393.188  6           2.233
## damagecause:county 227037485053054.625 36           1.583
## 
## Call:
## glm(formula = non_zero ~ year + damagecause * county, family = binomial(link = logit), 
##     data = alllevs2_apples)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.4991  -0.6581  -0.2455   0.6389   2.8325  
## 
## Coefficients:
##                                                         Estimate
## (Intercept)                                -1.911766275453498976
## year2002                                   -0.296492890701479161
## year2003                                    0.145706312891135559
## year2004                                   -0.761171384476088009
## year2005                                   -0.147263314168601001
## year2006                                   -0.448161974100270144
## year2007                                   -0.448161974100266203
## year2008                                   -1.092403236758539675
## year2009                                    0.719832845216727635
## year2010                                   -0.448161974100271643
## year2011                                    0.576970587656701173
## year2012                                   -1.855697555043593683
## year2013                                    1.006123780412798263
## year2014                                   -1.267668212480720147
## year2015                                    1.295604498595899434
## damagecauseCold Winter                     -0.813719026367579867
## damagecauseDrought                        -16.670795162752238383
## damagecauseFreeze                           2.267669275735777035
## damagecauseFrost                            3.693810087347036308
## damagecauseHail                             1.312972511828845334
## damagecauseHeat                             0.000000000000003276
## countyBenton                                2.581906773919941944
## countyDouglas                               0.950616770460329441
## countyFranklin                              2.267669275735789025
## countyGrant                                 1.958323056779491145
## countyUmatilla                              2.267669275735781476
## countyWalla Walla                           1.312972511828841560
## damagecauseCold Winter:countyBenton        -1.768187747552346423
## damagecauseDrought:countyBenton            -2.581906774552121142
## damagecauseFreeze:countyBenton             -1.155765962308678008
## damagecauseFrost:countyBenton              -2.581906773919936615
## damagecauseHail:countyBenton               -1.936556228969291249
## damagecauseHeat:countyBenton               -2.050748679623238591
## damagecauseCold Winter:countyDouglas       -0.950616770460338656
## damagecauseDrought:countyDouglas           14.906459365924293436
## damagecauseFreeze:countyDouglas            -1.259962989416622214
## damagecauseFrost:countyDouglas             -1.732135218393414666
## damagecauseHail:countyDouglas              -0.619785795977902620
## damagecauseHeat:countyDouglas              -0.419458676163631916
## damagecauseCold Winter:countyFranklin      -1.453950249368198833
## damagecauseDrought:countyFranklin          -2.267669276370001263
## damagecauseFreeze:countyFranklin           -0.841528464124530418
## damagecauseFrost:countyFranklin            -2.267669275735786805
## damagecauseHail:countyFranklin             -0.998735013644691971
## damagecauseHeat:countyFranklin             -2.267669275735781031
## damagecauseCold Winter:countyGrant         -1.958323056779501359
## damagecauseDrought:countyGrant             -1.958323057407937995
## damagecauseFreeze:countyGrant              -0.951714822318446285
## damagecauseFrost:countyGrant               -1.426154581047994974
## damagecauseHail:countyGrant                -0.359003929194383897
## damagecauseHeat:countyGrant                -1.958323056779487814
## damagecauseCold Winter:countyUmatilla      -1.453950249368192837
## damagecauseDrought:countyUmatilla          -2.267669276368539766
## damagecauseFreeze:countyUmatilla           -1.261061041274742056
## damagecauseFrost:countyUmatilla            -3.049187723668870476
## damagecauseHail:countyUmatilla             -2.267669275735785472
## damagecauseHeat:countyUmatilla             -2.267669275735777923
## damagecauseCold Winter:countyWalla Walla   -1.312972511828849775
## damagecauseDrought:countyWalla Walla       -1.312972512461034746
## damagecauseFreeze:countyWalla Walla        -2.267669275735777035
## damagecauseFrost:countyWalla Walla         -4.056165828715558419
## damagecauseHail:countyWalla Walla          -2.625945023657682675
## damagecauseHeat:countyWalla Walla          -1.312972511828838007
##                                                       Std. Error z value
## (Intercept)                                 0.872956650103049347  -2.190
## year2002                                    0.545003964148443543  -0.544
## year2003                                    0.539939138134612917   0.270
## year2004                                    0.555335276497485375  -1.371
## year2005                                    0.542821927559994144  -0.271
## year2006                                    0.547756927998779619  -0.818
## year2007                                    0.547756927998778953  -0.818
## year2008                                    0.566612520349545901  -1.928
## year2009                                    0.539281639708378724   1.335
## year2010                                    0.547756927998779619  -0.818
## year2011                                    0.538836225185700846   1.071
## year2012                                    0.610095709362365235  -3.042
## year2013                                    0.541449940600746915   1.858
## year2014                                    0.574191168755926462  -2.208
## year2015                                    0.545536228072138307   2.375
## damagecauseCold Winter                      1.319665926255276345  -0.617
## damagecauseDrought                       1588.404682624609904451  -0.010
## damagecauseFreeze                           0.968571951096577788   2.341
## damagecauseFrost                            1.047652421185483851   3.526
## damagecauseHail                             0.983928313989815062   1.334
## damagecauseHeat                             1.116243640191318498   0.000
## countyBenton                                0.974504964421534559   2.649
## countyDouglas                               1.004500237041336286   0.946
## countyFranklin                              0.968571951096581452   2.341
## countyGrant                                 0.967994122548203384   2.023
## countyUmatilla                              0.968571951096579675   2.341
## countyWalla Walla                           0.983928313989814063   1.334
## damagecauseCold Winter:countyBenton         1.639781933685468207  -1.078
## damagecauseDrought:countyBenton          2246.343378414106155105  -0.001
## damagecauseFreeze:countyBenton              1.310980993606898348  -0.882
## damagecauseFrost:countyBenton               1.369057088696661317  -1.886
## damagecauseHail:countyBenton                1.265052862040041859  -1.531
## damagecauseHeat:countyBenton                1.425678457600531246  -1.438
## damagecauseCold Winter:countyDouglas        1.801533938639166443  -0.528
## damagecauseDrought:countyDouglas         1588.405155571784689528   0.009
## damagecauseFreeze:countyDouglas             1.276690740680679337  -0.987
## damagecauseFrost:countyDouglas              1.347510681767840168  -1.285
## damagecauseHail:countyDouglas               1.293312425659092435  -0.479
## damagecauseHeat:countyDouglas               1.446820491910578044  -0.290
## damagecauseCold Winter:countyFranklin       1.636324356604436758  -0.889
## damagecauseDrought:countyFranklin        2246.343375850066877319  -0.001
## damagecauseFreeze:countyFranklin            1.306964727964921691  -0.644
## damagecauseFrost:countyFranklin             1.364840287681823083  -1.661
## damagecauseHail:countyFranklin              1.264082838521848773  -0.790
## damagecauseHeat:countyFranklin              1.477880742387085000  -1.534
## damagecauseCold Winter:countyGrant          1.781436618895128055  -1.099
## damagecauseDrought:countyGrant           2246.343375597620706685  -0.001
## damagecauseFreeze:countyGrant               1.276845294146106369  -0.745
## damagecauseFrost:countyGrant                1.422493174191510334  -1.003
## damagecauseHail:countyGrant                 1.273008588835026655  -0.282
## damagecauseHeat:countyGrant                 1.477502110169536920  -1.325
## damagecauseCold Winter:countyUmatilla       1.636324356604434094  -0.889
## damagecauseDrought:countyUmatilla        2246.343375848281993967  -0.001
## damagecauseFreeze:countyUmatilla            1.277014619185067978  -0.988
## damagecauseFrost:countyUmatilla             1.321574149005342758  -2.307
## damagecauseHail:countyUmatilla              1.274806607014817184  -1.779
## damagecauseHeat:countyUmatilla              1.477880742387085222  -1.534
## damagecauseCold Winter:countyWalla Walla    1.790144891600531807  -0.733
## damagecauseDrought:countyWalla Walla     2246.343382522070442064  -0.001
## damagecauseFreeze:countyWalla Walla         1.274806607014815851  -1.779
## damagecauseFrost:countyWalla Walla          1.352393169198307765  -2.999
## damagecauseHail:countyWalla Walla           1.392644815873095077  -1.886
## damagecauseHeat:countyWalla Walla           1.487990185229191464  -0.882
##                                          Pr(>|z|)    
## (Intercept)                              0.028525 *  
## year2002                                 0.586428    
## year2003                                 0.787270    
## year2004                                 0.170483    
## year2005                                 0.786166    
## year2006                                 0.413256    
## year2007                                 0.413256    
## year2008                                 0.053861 .  
## year2009                                 0.181942    
## year2010                                 0.413256    
## year2011                                 0.284272    
## year2012                                 0.002353 ** 
## year2013                                 0.063140 .  
## year2014                                 0.027262 *  
## year2015                                 0.017553 *  
## damagecauseCold Winter                   0.537492    
## damagecauseDrought                       0.991626    
## damagecauseFreeze                        0.019219 *  
## damagecauseFrost                         0.000422 ***
## damagecauseHail                          0.182067    
## damagecauseHeat                          1.000000    
## countyBenton                             0.008062 ** 
## countyDouglas                            0.343966    
## countyFranklin                           0.019219 *  
## countyGrant                              0.043066 *  
## countyUmatilla                           0.019219 *  
## countyWalla Walla                        0.182067    
## damagecauseCold Winter:countyBenton      0.280897    
## damagecauseDrought:countyBenton          0.999083    
## damagecauseFreeze:countyBenton           0.377991    
## damagecauseFrost:countyBenton            0.059308 .  
## damagecauseHail:countyBenton             0.125816    
## damagecauseHeat:countyBenton             0.150310    
## damagecauseCold Winter:countyDouglas     0.597728    
## damagecauseDrought:countyDouglas         0.992512    
## damagecauseFreeze:countyDouglas          0.323693    
## damagecauseFrost:countyDouglas           0.198641    
## damagecauseHail:countyDouglas            0.631780    
## damagecauseHeat:countyDouglas            0.771879    
## damagecauseCold Winter:countyFranklin    0.374247    
## damagecauseDrought:countyFranklin        0.999195    
## damagecauseFreeze:countyFranklin         0.519653    
## damagecauseFrost:countyFranklin          0.096615 .  
## damagecauseHail:countyFranklin           0.429477    
## damagecauseHeat:countyFranklin           0.124930    
## damagecauseCold Winter:countyGrant       0.271640    
## damagecauseDrought:countyGrant           0.999304    
## damagecauseFreeze:countyGrant            0.456052    
## damagecauseFrost:countyGrant             0.316066    
## damagecauseHail:countyGrant              0.777934    
## damagecauseHeat:countyGrant              0.185029    
## damagecauseCold Winter:countyUmatilla    0.374247    
## damagecauseDrought:countyUmatilla        0.999195    
## damagecauseFreeze:countyUmatilla         0.323394    
## damagecauseFrost:countyUmatilla          0.021041 *  
## damagecauseHail:countyUmatilla           0.075267 .  
## damagecauseHeat:countyUmatilla           0.124930    
## damagecauseCold Winter:countyWalla Walla 0.463287    
## damagecauseDrought:countyWalla Walla     0.999534    
## damagecauseFreeze:countyWalla Walla      0.075267 .  
## damagecauseFrost:countyWalla Walla       0.002706 ** 
## damagecauseHail:countyWalla Walla        0.059351 .  
## damagecauseHeat:countyWalla Walla        0.377571    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 946.38  on 734  degrees of freedom
## Residual deviance: 595.23  on 672  degrees of freedom
## AIC: 721.23
## 
## Number of Fisher Scoring iterations: 17

Now we run our mixed model analysis for these zero values.

##                                   GVIF Df GVIF^(1/(2*Df))
## year                             1.164 14           1.005
## damagecause            80589335779.706  6           8.107
## county                       15393.188  6           2.233
## damagecause:county 227037485053054.625 36           1.583
## 
## Call:
## glm(formula = non_zero ~ year + damagecause * county, family = binomial(link = logit), 
##     data = alllevs2_apples)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.4991  -0.6581  -0.2455   0.6389   2.8325  
## 
## Coefficients:
##                                                         Estimate
## (Intercept)                                -1.911766275453498976
## year2002                                   -0.296492890701479161
## year2003                                    0.145706312891135559
## year2004                                   -0.761171384476088009
## year2005                                   -0.147263314168601001
## year2006                                   -0.448161974100270144
## year2007                                   -0.448161974100266203
## year2008                                   -1.092403236758539675
## year2009                                    0.719832845216727635
## year2010                                   -0.448161974100271643
## year2011                                    0.576970587656701173
## year2012                                   -1.855697555043593683
## year2013                                    1.006123780412798263
## year2014                                   -1.267668212480720147
## year2015                                    1.295604498595899434
## damagecauseCold Winter                     -0.813719026367579867
## damagecauseDrought                        -16.670795162752238383
## damagecauseFreeze                           2.267669275735777035
## damagecauseFrost                            3.693810087347036308
## damagecauseHail                             1.312972511828845334
## damagecauseHeat                             0.000000000000003276
## countyBenton                                2.581906773919941944
## countyDouglas                               0.950616770460329441
## countyFranklin                              2.267669275735789025
## countyGrant                                 1.958323056779491145
## countyUmatilla                              2.267669275735781476
## countyWalla Walla                           1.312972511828841560
## damagecauseCold Winter:countyBenton        -1.768187747552346423
## damagecauseDrought:countyBenton            -2.581906774552121142
## damagecauseFreeze:countyBenton             -1.155765962308678008
## damagecauseFrost:countyBenton              -2.581906773919936615
## damagecauseHail:countyBenton               -1.936556228969291249
## damagecauseHeat:countyBenton               -2.050748679623238591
## damagecauseCold Winter:countyDouglas       -0.950616770460338656
## damagecauseDrought:countyDouglas           14.906459365924293436
## damagecauseFreeze:countyDouglas            -1.259962989416622214
## damagecauseFrost:countyDouglas             -1.732135218393414666
## damagecauseHail:countyDouglas              -0.619785795977902620
## damagecauseHeat:countyDouglas              -0.419458676163631916
## damagecauseCold Winter:countyFranklin      -1.453950249368198833
## damagecauseDrought:countyFranklin          -2.267669276370001263
## damagecauseFreeze:countyFranklin           -0.841528464124530418
## damagecauseFrost:countyFranklin            -2.267669275735786805
## damagecauseHail:countyFranklin             -0.998735013644691971
## damagecauseHeat:countyFranklin             -2.267669275735781031
## damagecauseCold Winter:countyGrant         -1.958323056779501359
## damagecauseDrought:countyGrant             -1.958323057407937995
## damagecauseFreeze:countyGrant              -0.951714822318446285
## damagecauseFrost:countyGrant               -1.426154581047994974
## damagecauseHail:countyGrant                -0.359003929194383897
## damagecauseHeat:countyGrant                -1.958323056779487814
## damagecauseCold Winter:countyUmatilla      -1.453950249368192837
## damagecauseDrought:countyUmatilla          -2.267669276368539766
## damagecauseFreeze:countyUmatilla           -1.261061041274742056
## damagecauseFrost:countyUmatilla            -3.049187723668870476
## damagecauseHail:countyUmatilla             -2.267669275735785472
## damagecauseHeat:countyUmatilla             -2.267669275735777923
## damagecauseCold Winter:countyWalla Walla   -1.312972511828849775
## damagecauseDrought:countyWalla Walla       -1.312972512461034746
## damagecauseFreeze:countyWalla Walla        -2.267669275735777035
## damagecauseFrost:countyWalla Walla         -4.056165828715558419
## damagecauseHail:countyWalla Walla          -2.625945023657682675
## damagecauseHeat:countyWalla Walla          -1.312972511828838007
##                                                       Std. Error z value
## (Intercept)                                 0.872956650103049347  -2.190
## year2002                                    0.545003964148443543  -0.544
## year2003                                    0.539939138134612917   0.270
## year2004                                    0.555335276497485375  -1.371
## year2005                                    0.542821927559994144  -0.271
## year2006                                    0.547756927998779619  -0.818
## year2007                                    0.547756927998778953  -0.818
## year2008                                    0.566612520349545901  -1.928
## year2009                                    0.539281639708378724   1.335
## year2010                                    0.547756927998779619  -0.818
## year2011                                    0.538836225185700846   1.071
## year2012                                    0.610095709362365235  -3.042
## year2013                                    0.541449940600746915   1.858
## year2014                                    0.574191168755926462  -2.208
## year2015                                    0.545536228072138307   2.375
## damagecauseCold Winter                      1.319665926255276345  -0.617
## damagecauseDrought                       1588.404682624609904451  -0.010
## damagecauseFreeze                           0.968571951096577788   2.341
## damagecauseFrost                            1.047652421185483851   3.526
## damagecauseHail                             0.983928313989815062   1.334
## damagecauseHeat                             1.116243640191318498   0.000
## countyBenton                                0.974504964421534559   2.649
## countyDouglas                               1.004500237041336286   0.946
## countyFranklin                              0.968571951096581452   2.341
## countyGrant                                 0.967994122548203384   2.023
## countyUmatilla                              0.968571951096579675   2.341
## countyWalla Walla                           0.983928313989814063   1.334
## damagecauseCold Winter:countyBenton         1.639781933685468207  -1.078
## damagecauseDrought:countyBenton          2246.343378414106155105  -0.001
## damagecauseFreeze:countyBenton              1.310980993606898348  -0.882
## damagecauseFrost:countyBenton               1.369057088696661317  -1.886
## damagecauseHail:countyBenton                1.265052862040041859  -1.531
## damagecauseHeat:countyBenton                1.425678457600531246  -1.438
## damagecauseCold Winter:countyDouglas        1.801533938639166443  -0.528
## damagecauseDrought:countyDouglas         1588.405155571784689528   0.009
## damagecauseFreeze:countyDouglas             1.276690740680679337  -0.987
## damagecauseFrost:countyDouglas              1.347510681767840168  -1.285
## damagecauseHail:countyDouglas               1.293312425659092435  -0.479
## damagecauseHeat:countyDouglas               1.446820491910578044  -0.290
## damagecauseCold Winter:countyFranklin       1.636324356604436758  -0.889
## damagecauseDrought:countyFranklin        2246.343375850066877319  -0.001
## damagecauseFreeze:countyFranklin            1.306964727964921691  -0.644
## damagecauseFrost:countyFranklin             1.364840287681823083  -1.661
## damagecauseHail:countyFranklin              1.264082838521848773  -0.790
## damagecauseHeat:countyFranklin              1.477880742387085000  -1.534
## damagecauseCold Winter:countyGrant          1.781436618895128055  -1.099
## damagecauseDrought:countyGrant           2246.343375597620706685  -0.001
## damagecauseFreeze:countyGrant               1.276845294146106369  -0.745
## damagecauseFrost:countyGrant                1.422493174191510334  -1.003
## damagecauseHail:countyGrant                 1.273008588835026655  -0.282
## damagecauseHeat:countyGrant                 1.477502110169536920  -1.325
## damagecauseCold Winter:countyUmatilla       1.636324356604434094  -0.889
## damagecauseDrought:countyUmatilla        2246.343375848281993967  -0.001
## damagecauseFreeze:countyUmatilla            1.277014619185067978  -0.988
## damagecauseFrost:countyUmatilla             1.321574149005342758  -2.307
## damagecauseHail:countyUmatilla              1.274806607014817184  -1.779
## damagecauseHeat:countyUmatilla              1.477880742387085222  -1.534
## damagecauseCold Winter:countyWalla Walla    1.790144891600531807  -0.733
## damagecauseDrought:countyWalla Walla     2246.343382522070442064  -0.001
## damagecauseFreeze:countyWalla Walla         1.274806607014815851  -1.779
## damagecauseFrost:countyWalla Walla          1.352393169198307765  -2.999
## damagecauseHail:countyWalla Walla           1.392644815873095077  -1.886
## damagecauseHeat:countyWalla Walla           1.487990185229191464  -0.882
##                                          Pr(>|z|)    
## (Intercept)                              0.028525 *  
## year2002                                 0.586428    
## year2003                                 0.787270    
## year2004                                 0.170483    
## year2005                                 0.786166    
## year2006                                 0.413256    
## year2007                                 0.413256    
## year2008                                 0.053861 .  
## year2009                                 0.181942    
## year2010                                 0.413256    
## year2011                                 0.284272    
## year2012                                 0.002353 ** 
## year2013                                 0.063140 .  
## year2014                                 0.027262 *  
## year2015                                 0.017553 *  
## damagecauseCold Winter                   0.537492    
## damagecauseDrought                       0.991626    
## damagecauseFreeze                        0.019219 *  
## damagecauseFrost                         0.000422 ***
## damagecauseHail                          0.182067    
## damagecauseHeat                          1.000000    
## countyBenton                             0.008062 ** 
## countyDouglas                            0.343966    
## countyFranklin                           0.019219 *  
## countyGrant                              0.043066 *  
## countyUmatilla                           0.019219 *  
## countyWalla Walla                        0.182067    
## damagecauseCold Winter:countyBenton      0.280897    
## damagecauseDrought:countyBenton          0.999083    
## damagecauseFreeze:countyBenton           0.377991    
## damagecauseFrost:countyBenton            0.059308 .  
## damagecauseHail:countyBenton             0.125816    
## damagecauseHeat:countyBenton             0.150310    
## damagecauseCold Winter:countyDouglas     0.597728    
## damagecauseDrought:countyDouglas         0.992512    
## damagecauseFreeze:countyDouglas          0.323693    
## damagecauseFrost:countyDouglas           0.198641    
## damagecauseHail:countyDouglas            0.631780    
## damagecauseHeat:countyDouglas            0.771879    
## damagecauseCold Winter:countyFranklin    0.374247    
## damagecauseDrought:countyFranklin        0.999195    
## damagecauseFreeze:countyFranklin         0.519653    
## damagecauseFrost:countyFranklin          0.096615 .  
## damagecauseHail:countyFranklin           0.429477    
## damagecauseHeat:countyFranklin           0.124930    
## damagecauseCold Winter:countyGrant       0.271640    
## damagecauseDrought:countyGrant           0.999304    
## damagecauseFreeze:countyGrant            0.456052    
## damagecauseFrost:countyGrant             0.316066    
## damagecauseHail:countyGrant              0.777934    
## damagecauseHeat:countyGrant              0.185029    
## damagecauseCold Winter:countyUmatilla    0.374247    
## damagecauseDrought:countyUmatilla        0.999195    
## damagecauseFreeze:countyUmatilla         0.323394    
## damagecauseFrost:countyUmatilla          0.021041 *  
## damagecauseHail:countyUmatilla           0.075267 .  
## damagecauseHeat:countyUmatilla           0.124930    
## damagecauseCold Winter:countyWalla Walla 0.463287    
## damagecauseDrought:countyWalla Walla     0.999534    
## damagecauseFreeze:countyWalla Walla      0.075267 .  
## damagecauseFrost:countyWalla Walla       0.002706 ** 
## damagecauseHail:countyWalla Walla        0.059351 .  
## damagecauseHeat:countyWalla Walla        0.377571    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 946.38  on 734  degrees of freedom
## Residual deviance: 595.23  on 672  degrees of freedom
## AIC: 721.23
## 
## Number of Fisher Scoring iterations: 17

Now subset to just those observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.

## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
##    Data: subset(alllevs2_apples, non_zero == 1)
## 
## REML criterion at convergence: 880.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.6105 -0.5833  0.1281  0.6038  3.2595 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  county   (Intercept) 0.4085   0.6391  
##  Residual             1.9353   1.3912  
## Number of obs: 253, groups:  county, 7
## 
## Fixed effects:
##                        Estimate Std. Error t value
## (Intercept)             10.0015     0.4420  22.627
## year2002                -0.5154     0.4851  -1.062
## year2003                 0.7557     0.4627   1.633
## year2004                -0.8494     0.5155  -1.648
## year2005                 0.4481     0.4732   0.947
## year2006                 0.6558     0.4989   1.315
## year2007                 1.3272     0.4906   2.705
## year2008                 0.3012     0.5431   0.555
## year2009                 1.4475     0.4465   3.242
## year2010                 0.6472     0.4902   1.320
## year2011                 0.5794     0.4467   1.297
## year2012                 0.8257     0.6462   1.278
## year2013                 1.9262     0.4366   4.412
## year2014                 1.1395     0.5637   2.021
## year2015                 1.5109     0.4388   3.444
## damagecauseCold Winter  -0.9218     0.5054  -1.824
## damagecauseDrought      -2.0524     1.4496  -1.416
## damagecauseFreeze        0.1111     0.2829   0.393
## damagecauseFrost         0.1800     0.2760   0.652
## damagecauseHail          0.5523     0.3164   1.746
## damagecauseHeat         -0.8392     0.4382  -1.915

Finally, we examine the coefficent estimates of our model output.

Hurdle Model - WHEAT

Here we run our hurdle technique for WHEAT Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?

##           llh       llhNull            G2      McFadden          r2ML 
## -1392.6347080 -1967.6122795  1149.9551430     0.2922210     0.3184041 
##          r2CU 
##     0.4357824
## 
##  Hosmer and Lemeshow goodness of fit (GOF) test
## 
## data:  alllevs2_wheat$non_zero, fitted(m1)
## X-squared = 8.0966, df = 8, p-value = 0.4241

##                    GVIF  Df GVIF^(1/(2*Df))
## year                NaN  14             NaN
## damagecause         NaN   7             NaN
## county              NaN  24             NaN
## damagecause:county  NaN 168             NaN
## 
## Call:
## glm(formula = non_zero ~ year + damagecause * county, family = binomial(link = logit), 
##     data = alllevs2_wheat)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.6627  -0.8038   0.2544   0.7952   2.3466  
## 
## Coefficients:
##                                                  Estimate  Std. Error
## (Intercept)                                      0.940273    0.689319
## year2002                                         0.029839    0.244296
## year2003                                        -0.521967    0.248805
## year2004                                        -0.029897    0.244533
## year2005                                        -0.364604    0.246987
## year2006                                         0.746722    0.246348
## year2007                                        -0.150204    0.245195
## year2008                                         1.126649    0.251419
## year2009                                         1.329795    0.255432
## year2010                                         0.996808    0.249345
## year2011                                         0.326554    0.244030
## year2012                                         1.126649    0.251419
## year2013                                         1.823089    0.269599
## year2014                                         1.260794    0.253960
## year2015                                         1.159745    0.252008
## damagecauseCold Winter                          17.169472 1600.457625
## damagecauseDecline in Price                     -0.406576    0.906276
## damagecauseDrought                              17.169473 1600.457590
## damagecauseFreeze                               17.169473 1600.457611
## damagecauseFrost                                17.169473 1600.457622
## damagecauseHail                                 -1.681886    0.865506
## damagecauseHeat                                 17.169473 1600.457629
## countyAsotin                                    -2.305719    0.883687
## countyBenewah                                   -1.681886    0.865506
## countyBenton                                    -2.305719    0.883687
## countyClearwater                                -1.077635    0.871151
## countyColumbia                                  -1.986128    0.871144
## countyDouglas                                   -1.382247    0.865513
## countyFranklin                                  -1.077635    0.871151
## countyGarfield                                  -2.305719    0.883687
## countyGilliam                                   -1.986128    0.871144
## countyGrant                                     -1.382247    0.865513
## countyIdaho                                     -0.757356    0.883656
## countyLatah                                     -1.077635    0.871151
## countyLewis                                     -0.757356    0.883656
## countyLincoln                                   -1.077635    0.871151
## countyMorrow                                    -1.681886    0.865506
## countyNez Perce                                 -1.382247    0.865513
## countySherman                                   -1.986128    0.871144
## countySpokane                                   -1.382247    0.865513
## countyUmatilla                                  -1.077635    0.871151
## countyUnion                                     -1.986128    0.871144
## countyWalla Walla                               -0.757356    0.883656
## countyWallowa                                   -1.681886    0.865506
## countyWasco                                     -1.382247    0.865513
## countyWhitman                                   -1.077635    0.871151
## damagecauseCold Winter:countyAsotin            -16.545639 1600.457823
## damagecauseDecline in Price:countyAsotin         0.726167    1.209533
## damagecauseDrought:countyAsotin                -13.549133 1600.458038
## damagecauseFreeze:countyAsotin                 -17.169473 1600.457819
## damagecauseFrost:countyAsotin                  -17.924943 1600.457866
## damagecauseHail:countyAsotin                     2.001477    1.179357
## damagecauseHeat:countyAsotin                   -13.549133 1600.458077
## damagecauseCold Winter:countyBenewah           -16.869833 1600.457813
## damagecauseDecline in Price:countyBenewah       -0.217257    1.205548
## damagecauseDrought:countyBenewah               -14.970792 1600.457874
## damagecauseFreeze:countyBenewah                -17.169473 1600.457799
## damagecauseFrost:countyBenewah                 -16.869834 1600.457810
## damagecauseHail:countyBenewah                   -0.213320    1.286916
## damagecauseHeat:countyBenewah                  -15.894162 1600.457840
## damagecauseCold Winter:countyBenton            -15.270329 1600.457846
## damagecauseDecline in Price:countyBenton         1.330048    1.205740
## damagecauseDrought:countyBenton                -14.346959 1600.457884
## damagecauseFreeze:countyBenton                 -15.621110 1600.457819
## damagecauseFrost:countyBenton                  -16.246001 1600.457820
## damagecauseHail:countyBenton                    -0.386697    1.477061
## damagecauseHeat:countyBenton                   -15.621110 1600.457837
## damagecauseCold Winter:countyClearwater        -18.747433 1600.457839
## damagecauseDecline in Price:countyClearwater    -1.171385    1.226445
## damagecauseDrought:countyClearwater            -17.169473 1600.457784
## damagecauseFreeze:countyClearwater             -19.153027 1600.457849
## damagecauseFrost:countyClearwater              -19.153027 1600.457859
## damagecauseHail:countyClearwater                 1.077635    1.165999
## damagecauseHeat:countyClearwater               -17.169473 1600.457823
## damagecauseCold Winter:countyColumbia          -17.489063 1600.457826
## damagecauseDecline in Price:countyColumbia       1.315069    1.200825
## damagecauseDrought:countyColumbia              -14.666550 1600.457877
## damagecauseFreeze:countyColumbia               -16.865230 1600.457802
## damagecauseFrost:countyColumbia                -16.565591 1600.457813
## damagecauseHail:countyColumbia                   0.606825    1.227182
## damagecauseHeat:countyColumbia                 -14.666550 1600.457916
## damagecauseCold Winter:countyDouglas           -15.270431 1600.457909
## damagecauseDecline in Price:countyDouglas        0.406576    1.192629
## damagecauseDrought:countyDouglas                 1.382247 2263.388820
## damagecauseFreeze:countyDouglas                -15.270431 1600.457895
## damagecauseFrost:countyDouglas                 -14.472605 1600.458060
## damagecauseHail:countyDouglas                    1.078005    1.165852
## damagecauseHeat:countyDouglas                  -15.270431 1600.457913
## damagecauseCold Winter:countyFranklin          -14.777217 1600.458067
## damagecauseDecline in Price:countyFranklin       1.077635    1.226779
## damagecauseDrought:countyFranklin                1.077635 2263.388822
## damagecauseFreeze:countyFranklin               -16.091838 1600.457848
## damagecauseFrost:countyFranklin                -14.777217 1600.458063
## damagecauseHail:countyFranklin                   1.077635    1.165999
## damagecauseHeat:countyFranklin                   1.077635 2263.388849
## damagecauseCold Winter:countyGarfield          -17.924943 1600.457869
## damagecauseDecline in Price:countyGarfield       1.330048    1.205740
## damagecauseDrought:countyGarfield              -13.549133 1600.458038
## damagecauseFreeze:countyGarfield               -15.941388 1600.457812
## damagecauseFrost:countyGarfield                -16.849882 1600.457823
## damagecauseHail:countyGarfield                   1.681886    1.188466
## damagecauseHeat:countyGarfield                 -13.549133 1600.458077
## damagecauseCold Winter:countyGilliam           -17.489063 1600.457826
## damagecauseDecline in Price:countyGilliam        1.315069    1.200825
## damagecauseDrought:countyGilliam               -13.868724 1600.458031
## damagecauseFreeze:countyGilliam                -16.865230 1600.457802
## damagecauseFrost:countyGilliam                 -17.489064 1600.457823
## damagecauseHail:countyGilliam                    1.362295    1.179203
## damagecauseHeat:countyGilliam                    1.986128 2263.388849
## damagecauseCold Winter:countyGrant             -16.193801 1600.457836
## damagecauseDecline in Price:countyGrant          1.031466    1.206028
## damagecauseDrought:countyGrant                   1.382247 2263.388819
## damagecauseFreeze:countyGrant                  -14.472605 1600.458049
## damagecauseFrost:countyGrant                     1.382247 2263.388842
## damagecauseHail:countyGrant                      0.758414    1.175116
## damagecauseHeat:countyGrant                    -14.472605 1600.458067
## damagecauseCold Winter:countyIdaho             -17.794363 1600.457823
## damagecauseDecline in Price:countyIdaho         -0.822196    1.209918
## damagecauseDrought:countyIdaho                 -15.895322 1600.457884
## damagecauseFreeze:countyIdaho                  -18.398244 1600.457812
## damagecauseFrost:countyIdaho                   -17.169473 1600.457830
## damagecauseHail:countyIdaho                      1.056995    1.175493
## damagecauseHeat:countyIdaho                    -16.412116 1600.457873
## damagecauseCold Winter:countyLatah             -17.773724 1600.457816
## damagecauseDecline in Price:countyLatah          0.101963    1.196778
## damagecauseDrought:countyLatah                 -15.575044 1600.457877
## damagecauseFreeze:countyLatah                  -17.474085 1600.457802
## damagecauseFrost:countyLatah                   -17.773724 1600.457813
## damagecauseHail:countyLatah                      0.453802    1.179308
## damagecauseHeat:countyLatah                    -16.091838 1600.457866
## damagecauseCold Winter:countyLewis             -18.094002 1600.457823
## damagecauseDecline in Price:countyLewis         -0.218315    1.205962
## damagecauseDrought:countyLewis                   0.757356 2263.388827
## damagecauseFreeze:countyLewis                  -18.717835 1600.457819
## damagecauseFrost:countyLewis                   -17.794363 1600.457820
## damagecauseHail:countyLewis                      0.453114    1.179417
## damagecauseHeat:countyLewis                    -16.412116 1600.457873
## damagecauseCold Winter:countyLincoln           -16.091838 1600.457862
## damagecauseDecline in Price:countyLincoln        1.077635    1.226779
## damagecauseDrought:countyLincoln                 1.077635 2263.388822
## damagecauseFreeze:countyLincoln                  1.077635 2263.388837
## damagecauseFrost:countyLincoln                   1.077635 2263.388844
## damagecauseHail:countyLincoln                    2.352945    1.197112
## damagecauseHeat:countyLincoln                    1.077635 2263.388849
## damagecauseCold Winter:countyMorrow            -17.169472 1600.457813
## damagecauseDecline in Price:countyMorrow         1.681886    1.222777
## damagecauseDrought:countyMorrow                -14.172966 1600.458028
## damagecauseFreeze:countyMorrow                 -15.487587 1600.457845
## damagecauseFrost:countyMorrow                  -15.894162 1600.457832
## damagecauseHail:countyMorrow                     1.377644    1.165830
## damagecauseHeat:countyMorrow                   -14.172966 1600.458067
## damagecauseCold Winter:countyNez Perce         -16.864860 1600.457816
## damagecauseDecline in Price:countyNez Perce      0.406576    1.192629
## damagecauseDrought:countyNez Perce               1.382247 2263.388820
## damagecauseFreeze:countyNez Perce              -17.469112 1600.457799
## damagecauseFrost:countyNez Perce               -17.773354 1600.457813
## damagecauseHail:countyNez Perce                  1.382247    1.161793
## damagecauseHeat:countyNez Perce                -15.787226 1600.457863
## damagecauseCold Winter:countySherman           -17.169472 1600.457819
## damagecauseDecline in Price:countySherman        1.986128    1.226774
## damagecauseDrought:countySherman               -13.868724 1600.458031
## damagecauseFreeze:countySherman                -16.565591 1600.457802
## damagecauseFrost:countySherman                 -18.760437 1600.457909
## damagecauseHail:countySherman                   -0.706288    1.469672
## damagecauseHeat:countySherman                  -13.868724 1600.458070
## damagecauseCold Winter:countySpokane           -16.544582 1600.457823
## damagecauseDecline in Price:countySpokane        0.711188    1.196811
## damagecauseDrought:countySpokane                 1.382247 2263.388820
## damagecauseFreeze:countySpokane                -16.544582 1600.457809
## damagecauseFrost:countySpokane                 -16.193801 1600.457832
## damagecauseHail:countySpokane                    1.681886    1.161950
## damagecauseHeat:countySpokane                    1.382247 2263.388847
## damagecauseCold Winter:countyUmatilla          -16.849194 1600.457826
## damagecauseDecline in Price:countyUmatilla       1.484210    1.257125
## damagecauseDrought:countyUmatilla              -14.777217 1600.458031
## damagecauseFreeze:countyUmatilla               -14.777217 1600.458053
## damagecauseFrost:countyUmatilla                -14.777217 1600.458063
## damagecauseHail:countyUmatilla                   1.681886    1.170467
## damagecauseHeat:countyUmatilla                   1.077635 2263.388849
## damagecauseCold Winter:countyUnion             -16.565591 1600.457816
## damagecauseDecline in Price:countyUnion          0.406576    1.200477
## damagecauseDrought:countyUnion                 -14.666550 1600.457877
## damagecauseFreeze:countyUnion                  -15.940701 1600.457812
## damagecauseFrost:countyUnion                   -16.260979 1600.457816
## damagecauseHail:countyUnion                      2.590379    1.170565
## damagecauseHeat:countyUnion                    -13.868724 1600.458070
## damagecauseCold Winter:countyWalla Walla       -17.169472 1600.457833
## damagecauseDecline in Price:countyWalla Walla    0.086297    1.210064
## damagecauseDrought:countyWalla Walla           -15.097496 1600.458038
## damagecauseFreeze:countyWalla Walla            -16.818692 1600.457832
## damagecauseFrost:countyWalla Walla             -15.895322 1600.457916
## damagecauseHail:countyWalla Walla                0.133523    1.188607
## damagecauseHeat:countyWalla Walla                0.757356 2263.388854
## damagecauseCold Winter:countyWallowa           -18.143182 1600.457836
## damagecauseDecline in Price:countyWallowa       -0.217257    1.205548
## damagecauseDrought:countyWallowa               -16.244943 1600.457788
## damagecauseFreeze:countyWallowa                -18.143182 1600.457822
## damagecauseFrost:countyWallowa                 -17.473715 1600.457813
## damagecauseHail:countyWallowa                    1.058053    1.175077
## damagecauseHeat:countyWallowa                  -16.565221 1600.457820
## damagecauseCold Winter:countyWasco             -17.469111 1600.457813
## damagecauseDecline in Price:countyWasco          1.031466    1.206028
## damagecauseDrought:countyWasco                 -15.270431 1600.457874
## damagecauseFreeze:countyWasco                  -16.193801 1600.457822
## damagecauseFrost:countyWasco                   -17.773354 1600.457813
## damagecauseHail:countyWasco                      0.002944    1.223318
## damagecauseHeat:countyWasco                    -14.472605 1600.458067
## damagecauseCold Winter:countyWhitman           -16.498413 1600.457839
## damagecauseDecline in Price:countyWhitman        1.077635    1.226779
## damagecauseDrought:countyWhitman                 1.077635 2263.388822
## damagecauseFreeze:countyWhitman                -16.498414 1600.457825
## damagecauseFrost:countyWhitman                 -14.777217 1600.458063
## damagecauseHail:countyWhitman                    1.681886    1.170467
## damagecauseHeat:countyWhitman                    1.077635 2263.388849
##                                               z value        Pr(>|z|)    
## (Intercept)                                     1.364         0.17255    
## year2002                                        0.122         0.90278    
## year2003                                       -2.098         0.03591 *  
## year2004                                       -0.122         0.90269    
## year2005                                       -1.476         0.13989    
## year2006                                        3.031         0.00244 ** 
## year2007                                       -0.613         0.54015    
## year2008                                        4.481 0.0000074238141 ***
## year2009                                        5.206 0.0000001928975 ***
## year2010                                        3.998 0.0000639570033 ***
## year2011                                        1.338         0.18084    
## year2012                                        4.481 0.0000074238141 ***
## year2013                                        6.762 0.0000000000136 ***
## year2014                                        4.965 0.0000006886671 ***
## year2015                                        4.602 0.0000041840555 ***
## damagecauseCold Winter                          0.011         0.99144    
## damagecauseDecline in Price                    -0.449         0.65370    
## damagecauseDrought                              0.011         0.99144    
## damagecauseFreeze                               0.011         0.99144    
## damagecauseFrost                                0.011         0.99144    
## damagecauseHail                                -1.943         0.05199 .  
## damagecauseHeat                                 0.011         0.99144    
## countyAsotin                                   -2.609         0.00908 ** 
## countyBenewah                                  -1.943         0.05199 .  
## countyBenton                                   -2.609         0.00908 ** 
## countyClearwater                               -1.237         0.21608    
## countyColumbia                                 -2.280         0.02261 *  
## countyDouglas                                  -1.597         0.11026    
## countyFranklin                                 -1.237         0.21608    
## countyGarfield                                 -2.609         0.00908 ** 
## countyGilliam                                  -2.280         0.02261 *  
## countyGrant                                    -1.597         0.11026    
## countyIdaho                                    -0.857         0.39141    
## countyLatah                                    -1.237         0.21608    
## countyLewis                                    -0.857         0.39141    
## countyLincoln                                  -1.237         0.21608    
## countyMorrow                                   -1.943         0.05199 .  
## countyNez Perce                                -1.597         0.11026    
## countySherman                                  -2.280         0.02261 *  
## countySpokane                                  -1.597         0.11026    
## countyUmatilla                                 -1.237         0.21608    
## countyUnion                                    -2.280         0.02261 *  
## countyWalla Walla                              -0.857         0.39141    
## countyWallowa                                  -1.943         0.05199 .  
## countyWasco                                    -1.597         0.11026    
## countyWhitman                                  -1.237         0.21608    
## damagecauseCold Winter:countyAsotin            -0.010         0.99175    
## damagecauseDecline in Price:countyAsotin        0.600         0.54826    
## damagecauseDrought:countyAsotin                -0.008         0.99325    
## damagecauseFreeze:countyAsotin                 -0.011         0.99144    
## damagecauseFrost:countyAsotin                  -0.011         0.99106    
## damagecauseHail:countyAsotin                    1.697         0.08968 .  
## damagecauseHeat:countyAsotin                   -0.008         0.99325    
## damagecauseCold Winter:countyBenewah           -0.011         0.99159    
## damagecauseDecline in Price:countyBenewah      -0.180         0.85698    
## damagecauseDrought:countyBenewah               -0.009         0.99254    
## damagecauseFreeze:countyBenewah                -0.011         0.99144    
## damagecauseFrost:countyBenewah                 -0.011         0.99159    
## damagecauseHail:countyBenewah                  -0.166         0.86835    
## damagecauseHeat:countyBenewah                  -0.010         0.99208    
## damagecauseCold Winter:countyBenton            -0.010         0.99239    
## damagecauseDecline in Price:countyBenton        1.103         0.26999    
## damagecauseDrought:countyBenton                -0.009         0.99285    
## damagecauseFreeze:countyBenton                 -0.010         0.99221    
## damagecauseFrost:countyBenton                  -0.010         0.99190    
## damagecauseHail:countyBenton                   -0.262         0.79347    
## damagecauseHeat:countyBenton                   -0.010         0.99221    
## damagecauseCold Winter:countyClearwater        -0.012         0.99065    
## damagecauseDecline in Price:countyClearwater   -0.955         0.33952    
## damagecauseDrought:countyClearwater            -0.011         0.99144    
## damagecauseFreeze:countyClearwater             -0.012         0.99045    
## damagecauseFrost:countyClearwater              -0.012         0.99045    
## damagecauseHail:countyClearwater                0.924         0.35537    
## damagecauseHeat:countyClearwater               -0.011         0.99144    
## damagecauseCold Winter:countyColumbia          -0.011         0.99128    
## damagecauseDecline in Price:countyColumbia      1.095         0.27346    
## damagecauseDrought:countyColumbia              -0.009         0.99269    
## damagecauseFreeze:countyColumbia               -0.011         0.99159    
## damagecauseFrost:countyColumbia                -0.010         0.99174    
## damagecauseHail:countyColumbia                  0.494         0.62096    
## damagecauseHeat:countyColumbia                 -0.009         0.99269    
## damagecauseCold Winter:countyDouglas           -0.010         0.99239    
## damagecauseDecline in Price:countyDouglas       0.341         0.73317    
## damagecauseDrought:countyDouglas                0.001         0.99951    
## damagecauseFreeze:countyDouglas                -0.010         0.99239    
## damagecauseFrost:countyDouglas                 -0.009         0.99278    
## damagecauseHail:countyDouglas                   0.925         0.35515    
## damagecauseHeat:countyDouglas                  -0.010         0.99239    
## damagecauseCold Winter:countyFranklin          -0.009         0.99263    
## damagecauseDecline in Price:countyFranklin      0.878         0.37971    
## damagecauseDrought:countyFranklin               0.000         0.99962    
## damagecauseFreeze:countyFranklin               -0.010         0.99198    
## damagecauseFrost:countyFranklin                -0.009         0.99263    
## damagecauseHail:countyFranklin                  0.924         0.35537    
## damagecauseHeat:countyFranklin                  0.000         0.99962    
## damagecauseCold Winter:countyGarfield          -0.011         0.99106    
## damagecauseDecline in Price:countyGarfield      1.103         0.26999    
## damagecauseDrought:countyGarfield              -0.008         0.99325    
## damagecauseFreeze:countyGarfield               -0.010         0.99205    
## damagecauseFrost:countyGarfield                -0.011         0.99160    
## damagecauseHail:countyGarfield                  1.415         0.15702    
## damagecauseHeat:countyGarfield                 -0.008         0.99325    
## damagecauseCold Winter:countyGilliam           -0.011         0.99128    
## damagecauseDecline in Price:countyGilliam       1.095         0.27346    
## damagecauseDrought:countyGilliam               -0.009         0.99309    
## damagecauseFreeze:countyGilliam                -0.011         0.99159    
## damagecauseFrost:countyGilliam                 -0.011         0.99128    
## damagecauseHail:countyGilliam                   1.155         0.24798    
## damagecauseHeat:countyGilliam                   0.001         0.99930    
## damagecauseCold Winter:countyGrant             -0.010         0.99193    
## damagecauseDecline in Price:countyGrant         0.855         0.39241    
## damagecauseDrought:countyGrant                  0.001         0.99951    
## damagecauseFreeze:countyGrant                  -0.009         0.99278    
## damagecauseFrost:countyGrant                    0.001         0.99951    
## damagecauseHail:countyGrant                     0.645         0.51867    
## damagecauseHeat:countyGrant                    -0.009         0.99278    
## damagecauseCold Winter:countyIdaho             -0.011         0.99113    
## damagecauseDecline in Price:countyIdaho        -0.680         0.49679    
## damagecauseDrought:countyIdaho                 -0.010         0.99208    
## damagecauseFreeze:countyIdaho                  -0.011         0.99083    
## damagecauseFrost:countyIdaho                   -0.011         0.99144    
## damagecauseHail:countyIdaho                     0.899         0.36855    
## damagecauseHeat:countyIdaho                    -0.010         0.99182    
## damagecauseCold Winter:countyLatah             -0.011         0.99114    
## damagecauseDecline in Price:countyLatah         0.085         0.93210    
## damagecauseDrought:countyLatah                 -0.010         0.99224    
## damagecauseFreeze:countyLatah                  -0.011         0.99129    
## damagecauseFrost:countyLatah                   -0.011         0.99114    
## damagecauseHail:countyLatah                     0.385         0.70038    
## damagecauseHeat:countyLatah                    -0.010         0.99198    
## damagecauseCold Winter:countyLewis             -0.011         0.99098    
## damagecauseDecline in Price:countyLewis        -0.181         0.85634    
## damagecauseDrought:countyLewis                  0.000         0.99973    
## damagecauseFreeze:countyLewis                  -0.012         0.99067    
## damagecauseFrost:countyLewis                   -0.011         0.99113    
## damagecauseHail:countyLewis                     0.384         0.70084    
## damagecauseHeat:countyLewis                    -0.010         0.99182    
## damagecauseCold Winter:countyLincoln           -0.010         0.99198    
## damagecauseDecline in Price:countyLincoln       0.878         0.37971    
## damagecauseDrought:countyLincoln                0.000         0.99962    
## damagecauseFreeze:countyLincoln                 0.000         0.99962    
## damagecauseFrost:countyLincoln                  0.000         0.99962    
## damagecauseHail:countyLincoln                   1.966         0.04935 *  
## damagecauseHeat:countyLincoln                   0.000         0.99962    
## damagecauseCold Winter:countyMorrow            -0.011         0.99144    
## damagecauseDecline in Price:countyMorrow        1.375         0.16899    
## damagecauseDrought:countyMorrow                -0.009         0.99293    
## damagecauseFreeze:countyMorrow                 -0.010         0.99228    
## damagecauseFrost:countyMorrow                  -0.010         0.99208    
## damagecauseHail:countyMorrow                    1.182         0.23733    
## damagecauseHeat:countyMorrow                   -0.009         0.99293    
## damagecauseCold Winter:countyNez Perce         -0.011         0.99159    
## damagecauseDecline in Price:countyNez Perce     0.341         0.73317    
## damagecauseDrought:countyNez Perce              0.001         0.99951    
## damagecauseFreeze:countyNez Perce              -0.011         0.99129    
## damagecauseFrost:countyNez Perce               -0.011         0.99114    
## damagecauseHail:countyNez Perce                 1.190         0.23414    
## damagecauseHeat:countyNez Perce                -0.010         0.99213    
## damagecauseCold Winter:countySherman           -0.011         0.99144    
## damagecauseDecline in Price:countySherman       1.619         0.10545    
## damagecauseDrought:countySherman               -0.009         0.99309    
## damagecauseFreeze:countySherman                -0.010         0.99174    
## damagecauseFrost:countySherman                 -0.012         0.99065    
## damagecauseHail:countySherman                  -0.481         0.63082    
## damagecauseHeat:countySherman                  -0.009         0.99309    
## damagecauseCold Winter:countySpokane           -0.010         0.99175    
## damagecauseDecline in Price:countySpokane       0.594         0.55235    
## damagecauseDrought:countySpokane                0.001         0.99951    
## damagecauseFreeze:countySpokane                -0.010         0.99175    
## damagecauseFrost:countySpokane                 -0.010         0.99193    
## damagecauseHail:countySpokane                   1.447         0.14777    
## damagecauseHeat:countySpokane                   0.001         0.99951    
## damagecauseCold Winter:countyUmatilla          -0.011         0.99160    
## damagecauseDecline in Price:countyUmatilla      1.181         0.23775    
## damagecauseDrought:countyUmatilla              -0.009         0.99263    
## damagecauseFreeze:countyUmatilla               -0.009         0.99263    
## damagecauseFrost:countyUmatilla                -0.009         0.99263    
## damagecauseHail:countyUmatilla                  1.437         0.15074    
## damagecauseHeat:countyUmatilla                  0.000         0.99962    
## damagecauseCold Winter:countyUnion             -0.010         0.99174    
## damagecauseDecline in Price:countyUnion         0.339         0.73485    
## damagecauseDrought:countyUnion                 -0.009         0.99269    
## damagecauseFreeze:countyUnion                  -0.010         0.99205    
## damagecauseFrost:countyUnion                   -0.010         0.99189    
## damagecauseHail:countyUnion                     2.213         0.02690 *  
## damagecauseHeat:countyUnion                    -0.009         0.99309    
## damagecauseCold Winter:countyWalla Walla       -0.011         0.99144    
## damagecauseDecline in Price:countyWalla Walla   0.071         0.94315    
## damagecauseDrought:countyWalla Walla           -0.009         0.99247    
## damagecauseFreeze:countyWalla Walla            -0.011         0.99162    
## damagecauseFrost:countyWalla Walla             -0.010         0.99208    
## damagecauseHail:countyWalla Walla               0.112         0.91056    
## damagecauseHeat:countyWalla Walla               0.000         0.99973    
## damagecauseCold Winter:countyWallowa           -0.011         0.99096    
## damagecauseDecline in Price:countyWallowa      -0.180         0.85698    
## damagecauseDrought:countyWallowa               -0.010         0.99190    
## damagecauseFreeze:countyWallowa                -0.011         0.99096    
## damagecauseFrost:countyWallowa                 -0.011         0.99129    
## damagecauseHail:countyWallowa                   0.900         0.36790    
## damagecauseHeat:countyWallowa                  -0.010         0.99174    
## damagecauseCold Winter:countyWasco             -0.011         0.99129    
## damagecauseDecline in Price:countyWasco         0.855         0.39241    
## damagecauseDrought:countyWasco                 -0.010         0.99239    
## damagecauseFreeze:countyWasco                  -0.010         0.99193    
## damagecauseFrost:countyWasco                   -0.011         0.99114    
## damagecauseHail:countyWasco                     0.002         0.99808    
## damagecauseHeat:countyWasco                    -0.009         0.99278    
## damagecauseCold Winter:countyWhitman           -0.010         0.99178    
## damagecauseDecline in Price:countyWhitman       0.878         0.37971    
## damagecauseDrought:countyWhitman                0.000         0.99962    
## damagecauseFreeze:countyWhitman                -0.010         0.99178    
## damagecauseFrost:countyWhitman                 -0.009         0.99263    
## damagecauseHail:countyWhitman                   1.437         0.15074    
## damagecauseHeat:countyWhitman                   0.000         0.99962    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 3935.2  on 2999  degrees of freedom
## Residual deviance: 2785.3  on 2786  degrees of freedom
## AIC: 3213.3
## 
## Number of Fisher Scoring iterations: 17